UOWHFs from OWFs: Trading Regularity for Efficiency

  • Kfir Barhum
  • Ueli Maurer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7533)


A universal one-way hash function (UOWHF) is a shrinking function for which finding a second preimage is infeasible. A UOWHF, a fundamental cryptographic primitive from which digital signature can be obtained, can be constructed from any one-way function (OWF). The best known construction from any OWF f:{0,1} n  → {0,1} n , due to Haitner et. al. [2], has output length Õ(n 7) and Õ(n 5) for the uniform and non-uniform models, respectively. On the other hand, if the OWF is known to be injective, i.e., maximally regular, the Naor-Yung construction is simple and practical with output length linear in that of the OWF, and making only one query to the underlying OWF.

In this paper, we establish a trade-off between the efficiency of the construction and the assumption about the regularity of the OWF f. Our first result is a construction comparably efficient to the Naor-Yung construction but applicable to any close-to-regular function. A second result shows that if |f − 1 f(x)| is concentrated on an interval of size 2 s(n), the construction obtained has output length Õ(n·s(n)6) and Õ(n ·s(n)4) for the uniform and non-uniform models, respectively.


Complexity-Based Cryptography One-Way Functions Universal One-Way Hash Functions Computational Entropy 


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  1. 1.
    Goldreich, O., Krawczyk, H., Luby, M.: On the existence of pseudorandom generators. SIAM J. Comput. 22(6), 1163–1175 (1993)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Haitner, I., Holenstein, T., Reingold, O., Vadhan, S., Wee, H.: Universal One-Way Hash Functions via Inaccessible Entropy. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 616–637. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  3. 3.
    Haitner, I., Nguyen, M.-H., Ong, S.J., Reingold, O., Vadhan, S.P.: Statistically hiding commitments and statistical zero-knowledge arguments from any one-way function. SIAM J. Comput. 39(3), 1153–1218 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Haitner, I., Reingold, O., Vadhan, S.P.: Efficiency improvements in constructing pseudorandom generators from one-way functions. In: Schulman, L.J. (ed.) STOC, pp. 437–446. ACM (2010)Google Scholar
  5. 5.
    Haitner, I., Reingold, O., Vadhan, S.P., Wee, H.: Inaccessible entropy. In: Mitzenmacher, M. (ed.) STOC, pp. 611–620. ACM (2009)Google Scholar
  6. 6.
    Naor, M., Yung, M.: Universal one-way hash functions and their cryptographic applications. In: STOC, pp. 33–43. ACM (1989)Google Scholar
  7. 7.
    Rompel, J.: One-way functions are necessary and sufficient for secure signatures. In: STOC, pp. 387–394. ACM (1990)Google Scholar
  8. 8.
    De Santis, A., Yung, M.: On the Design of Provably-Secure Cryptographic Hash Functions. In: Damgård, I.B. (ed.) EUROCRYPT 1990. LNCS, vol. 473, pp. 412–431. Springer, Heidelberg (1991)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Kfir Barhum
    • 1
  • Ueli Maurer
    • 1
  1. 1.Department of Computer ScienceETH ZurichZurichSwitzerland

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